Details

Time bar (total: 2.0min)

analyze1.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
100%0%0%2
Compiler

Compiled 8 to 6 computations (25% saved)

sample10.0ms (0%)

Algorithm
intervals
Results
6.0ms256×body128valid
Compiler

Compiled 15 to 12 computations (20% saved)

simplify96.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0810
1810

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
14.2b
Counts
2 → 1
Compiler

Compiled 7 to 5 computations (28.6% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

14.2b
(/.f64 x (+.f64 (*.f64 x x) 1))
14.2b
(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite8.0ms (0%)

Algorithm
rewrite-expression-head
Rules
times-frac_binary64_1448 add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
associate-/r*_binary64_1386 add-cbrt-cube_binary64_1478 associate-/l*_binary64_1387 add-exp-log_binary64_1480
associate-/r/_binary64_1388
cbrt-undiv_binary64_1476 div-inv_binary64_1439 clear-num_binary64_1441 add-log-exp_binary64_1481 frac-2neg_binary64_1453 flip3-+_binary64_1445 flip-+_binary64_1416 pow1_binary64_1503 div-exp_binary64_1493
Counts
1 → 29
Calls

2 calls:

6.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))
0.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))

series55.0ms (0%)

Counts
1 → 12
Calls

1 calls:

55.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))
Compiler

Compiled 124 to 106 computations (14.5% saved)

simplify76.0ms (0.1%)

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
05088673

prune157.0ms (0.1%)

Pruning

33 alts after pruning (32 fresh and 1 done)

PrunedKeptTotal
New93241
Fresh000
Picked000
Done011
Total93342
Error
0b
Counts
42 → 33
Compiler

Compiled 912 to 565 computations (38% saved)

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

14.2b
(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.2b
(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0b
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
14.2b
(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.2b
(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite59.0ms (0%)

Algorithm
rewrite-expression-head
Rules
270×times-frac_binary64_1448
148×add-sqr-sqrt_binary64_1464
146×add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
144×sqrt-prod_binary64_1458
24×associate-/l*_binary64_1387
20×sqrt-div_binary64_1459
16×associate-/r/_binary64_1388
10×flip3-+_binary64_1445 flip-+_binary64_1416
add-cbrt-cube_binary64_1478 div-inv_binary64_1439 add-exp-log_binary64_1480
associate-/r*_binary64_1386
pow1_binary64_1503
cbrt-undiv_binary64_1476 add-log-exp_binary64_1481 div-exp_binary64_1493
sqrt-pow1_binary64_1460 rem-sqrt-square_binary64_1455 pow1/2_binary64_1522
associate-/l/_binary64_1389 clear-num_binary64_1441 frac-2neg_binary64_1453
Counts
3 → 221
Calls

6 calls:

17.0ms
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0ms
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))

series154.0ms (0.1%)

Counts
3 → 34
Calls

3 calls:

61.0ms
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
48.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
44.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
Compiler

Compiled 610 to 492 computations (19.3% saved)

simplify153.0ms (0.1%)

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
049867938
149867938

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b
(pow.f64 (/.f64 1 x) 3)
0.3b
(pow.f64 (/.f64 1 x) 3)

rewrite9.0ms (0%)

Algorithm
rewrite-expression-head
Rules
18×times-frac_binary64_1448
16×add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
13×cube-prod_binary64_1470 unpow-prod-down_binary64_1521
add-exp-log_binary64_1480
add-cbrt-cube_binary64_1478 pow-exp_binary64_1510
pow-unpow_binary64_1519 pow1_binary64_1503 pow-pow_binary64_1514
div-inv_binary64_1439 rem-cube-cbrt_binary64_1465 div-exp_binary64_1493
inv-pow_binary64_1527 cbrt-undiv_binary64_1476 cube-mult_binary64_1472 1-exp_binary64_1486 rec-exp_binary64_1492 add-log-exp_binary64_1481 pow-flip_binary64_1516 sqr-pow_binary64_1414 unpow3_binary64_1508 cube-div_binary64_1471 pow-to-exp_binary64_1511
Counts
1 → 50
Calls

2 calls:

5.0ms
(pow.f64 (/.f64 1 x) 3)
0.0ms
(pow.f64 (/.f64 1 x) 3)

series29.0ms (0%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(pow.f64 (/.f64 1 x) 3)
Compiler

Compiled 54 to 48 computations (11.1% saved)

simplify75.0ms (0.1%)

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
05406472

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

5.6b
(/.f64 (sqrt.f64 x) (/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x)))
2.2b
(/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x))
2.2b
(/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x))
5.6b
(/.f64 (sqrt.f64 x) (/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x)))

rewrite45.0ms (0%)

Algorithm
rewrite-expression-head
Rules
276×times-frac_binary64_1448
154×add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
144×sqrt-prod_binary64_1458
28×associate-/r*_binary64_1386
add-cbrt-cube_binary64_1478 div-inv_binary64_1439 associate-/l*_binary64_1387 add-exp-log_binary64_1480
cbrt-undiv_binary64_1476 div-exp_binary64_1493
associate-/l/_binary64_1389 clear-num_binary64_1441 add-log-exp_binary64_1481 frac-2neg_binary64_1453 pow1_binary64_1503
associate-/r/_binary64_1388 flip3-+_binary64_1445 flip-+_binary64_1416
Counts
2 → 216
Calls

4 calls:

13.0ms
(/.f64 (sqrt.f64 x) (/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x)))
7.0ms
(/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x))
0.0ms
(/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x))
0.0ms
(/.f64 (sqrt.f64 x) (/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x)))

series64.0ms (0.1%)

Counts
2 → 12
Calls

2 calls:

47.0ms
(/.f64 (sqrt.f64 x) (/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x)))
16.0ms
(/.f64 (+.f64 (*.f64 x x) 1) (sqrt.f64 x))
Compiler

Compiled 150 to 127 computations (15.3% saved)

simplify114.0ms (0.1%)

Algorithm
egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049706578
149706578

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
0.5b
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
2.7b
(/.f64 (cbrt.f64 x) (+.f64 (*.f64 x x) 1))
11.5b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 (*.f64 x x) 1)))

rewrite35.0ms (0%)

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt_binary64_1464
38×times-frac_binary64_1448
34×add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
28×cbrt-prod_binary64_1473
24×associate-*r*_binary64_1382
18×add-exp-log_binary64_1480
11×add-cbrt-cube_binary64_1478
pow1_binary64_1503
cbrt-unprod_binary64_1475 associate-/l*_binary64_1387 prod-exp_binary64_1491
associate-/r/_binary64_1388 add-log-exp_binary64_1481
cbrt-undiv_binary64_1476 associate-/r*_binary64_1386 pow-prod-down_binary64_1513 div-exp_binary64_1493 unswap-sqr_binary64_1410
div-inv_binary64_1439 flip3-+_binary64_1445 flip-+_binary64_1416 pow1/3_binary64_1524
associate-*r/_binary64_1384 clear-num_binary64_1441 associate-*l*_binary64_1383 *-commutative_binary64_1373 frac-2neg_binary64_1453
Counts
4 → 110
Calls

8 calls:

17.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 (*.f64 x x) 1)))
6.0ms
(/.f64 (cbrt.f64 x) (+.f64 (*.f64 x x) 1))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
0.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))

series345.0ms (0.3%)

Counts
4 → 27
Calls

4 calls:

101.0ms
(/.f64 (cbrt.f64 x) (+.f64 (*.f64 x x) 1))
92.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 (*.f64 x x) 1)))
78.0ms
(cbrt.f64 x)
74.0ms
(cbrt.f64 x)
Compiler

Compiled 571 to 450 computations (21.2% saved)

simplify107.0ms (0.1%)

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
049122225
149122225

prune6.3s (5.2%)

Pruning

257 alts after pruning (251 fresh and 6 done)

PrunedKeptTotal
New443230673
Fresh62127
Picked000
Done066
Total449257706
Error
0b
Counts
706 → 257
Compiler

Compiled 13495 to 7704 computations (42.9% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

14.2b
(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.2b
(pow.f64 (+.f64 (*.f64 x x) 1) 1/2)
0.0b
(/.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 x x) 1) 1/2)) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b
(/.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 x x) 1) 1/2)) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
14.2b
(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.2b
(pow.f64 (+.f64 (*.f64 x x) 1) 1/2)

rewrite62.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
297×times-frac_binary64_1448
157×add-sqr-sqrt_binary64_1464
156×add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
81×sqrt-prod_binary64_1458
66×unpow-prod-down_binary64_1521
25×associate-/l*_binary64_1387
22×sqr-pow_binary64_1414
14×add-exp-log_binary64_1480
add-cbrt-cube_binary64_1478 div-inv_binary64_1439
div-exp_binary64_1493
associate-/r*_binary64_1386
pow1_binary64_1503
sqrt-div_binary64_1459
cbrt-undiv_binary64_1476 pow-unpow_binary64_1519 add-log-exp_binary64_1481
pow-exp_binary64_1510 associate-/r/_binary64_1388 flip3-+_binary64_1445 flip-+_binary64_1416 pow-to-exp_binary64_1511
sqrt-pow1_binary64_1460 rem-sqrt-square_binary64_1455 associate-/l/_binary64_1389 clear-num_binary64_1441 frac-2neg_binary64_1453 unpow1/2_binary64_1506 pow1/2_binary64_1522 pow-pow_binary64_1514
Counts
3 → 233
Calls

6 calls:

18.0ms
(/.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 x x) 1) 1/2)) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms
(pow.f64 (+.f64 (*.f64 x x) 1) 1/2)
4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0ms
(/.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 x x) 1) 1/2)) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0ms
(pow.f64 (+.f64 (*.f64 x x) 1) 1/2)

series196.0ms (0.2%)

Counts
3 → 34
Calls

3 calls:

89.0ms
(pow.f64 (+.f64 (*.f64 x x) 1) 1/2)
56.0ms
(/.f64 (/.f64 x (pow.f64 (+.f64 (*.f64 x x) 1) 1/2)) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
51.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
Compiler

Compiled 622 to 504 computations (19% saved)

simplify121.0ms (0.1%)

Algorithm
egg-herbie
Counts
267 → 267
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
050028253

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

14.2b
(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))
14.2b
(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))

rewrite12.0ms (0%)

Algorithm
rewrite-expression-head
Rules
40×times-frac_binary64_1448
38×add-sqr-sqrt_binary64_1464
27×add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
15×distribute-lft-neg-in_binary64_1399 distribute-rgt-neg-in_binary64_1400
11×difference-of-squares_binary64_1411
10×associate-/l*_binary64_1387
neg-mul-1_binary64_1438
associate-/r*_binary64_1386
add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
associate-/r/_binary64_1388
cbrt-undiv_binary64_1476 div-inv_binary64_1439 clear-num_binary64_1441 flip3--_binary64_1446 add-log-exp_binary64_1481 flip--_binary64_1417 frac-2neg_binary64_1453 distribute-frac-neg_binary64_1405 pow1_binary64_1503 div-sub_binary64_1447 neg-sub0_binary64_1437 div-exp_binary64_1493
Counts
1 → 70
Calls

2 calls:

6.0ms
(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))
0.0ms
(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))

series62.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

62.0ms
(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))
Compiler

Compiled 124 to 106 computations (14.5% saved)

simplify91.0ms (0.1%)

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049161643
149161643

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

1.4b
(pow.f64 (/.f64 1 x) (sqrt.f64 3))
0.8b
(pow.f64 (pow.f64 (/.f64 1 x) (sqrt.f64 3)) (sqrt.f64 3))
0.8b
(pow.f64 (pow.f64 (/.f64 1 x) (sqrt.f64 3)) (sqrt.f64 3))
1.4b
(pow.f64 (/.f64 1 x) (sqrt.f64 3))

rewrite18.0ms (0%)

Algorithm
rewrite-expression-head
Rules
43×unpow-prod-down_binary64_1521
21×add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
18×times-frac_binary64_1448
14×pow-exp_binary64_1510
13×add-exp-log_binary64_1480
12×pow-unpow_binary64_1519
sqrt-prod_binary64_1458
pow1_binary64_1503 div-exp_binary64_1493 pow-pow_binary64_1514
sqr-pow_binary64_1414 pow-to-exp_binary64_1511
add-cbrt-cube_binary64_1478 div-inv_binary64_1439 1-exp_binary64_1486 rec-exp_binary64_1492 add-log-exp_binary64_1481
inv-pow_binary64_1527 pow-flip_binary64_1516
Counts
2 → 74
Calls

4 calls:

7.0ms
(pow.f64 (pow.f64 (/.f64 1 x) (sqrt.f64 3)) (sqrt.f64 3))
5.0ms
(pow.f64 (/.f64 1 x) (sqrt.f64 3))
0.0ms
(pow.f64 (pow.f64 (/.f64 1 x) (sqrt.f64 3)) (sqrt.f64 3))
0.0ms
(pow.f64 (/.f64 1 x) (sqrt.f64 3))

series269.0ms (0.2%)

Counts
2 → 6
Calls

2 calls:

183.0ms
(pow.f64 (pow.f64 (/.f64 1 x) (sqrt.f64 3)) (sqrt.f64 3))
86.0ms
(pow.f64 (/.f64 1 x) (sqrt.f64 3))
Compiler

Compiled 184 to 172 computations (6.5% saved)

simplify94.0ms (0.1%)

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
050131340

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(cbrt.f64 x)
0.5b
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.3b
(cbrt.f64 (sqrt.f64 x))
0.3b
(cbrt.f64 (sqrt.f64 x))
0.5b
(cbrt.f64 x)
0.5b
(/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x)))
1.1b
(/.f64 (cbrt.f64 (sqrt.f64 x)) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x))))
6.1b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 x)) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x)))))

rewrite242.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
1119×times-frac_binary64_1448
761×cbrt-prod_binary64_1473
612×add-sqr-sqrt_binary64_1464
578×add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
379×sqrt-prod_binary64_1458
284×associate-*r*_binary64_1382
40×associate-/r*_binary64_1386
32×add-exp-log_binary64_1480
22×div-inv_binary64_1439
16×add-cbrt-cube_binary64_1478
13×unswap-sqr_binary64_1410
12×associate-/l*_binary64_1387
10×cbrt-undiv_binary64_1476 div-exp_binary64_1493
cbrt-unprod_binary64_1475 prod-exp_binary64_1491 pow1_binary64_1503
add-log-exp_binary64_1481
pow-prod-down_binary64_1513
associate-/l/_binary64_1389 associate-/r/_binary64_1388 clear-num_binary64_1441 frac-2neg_binary64_1453
associate-*r/_binary64_1384 associate-*l*_binary64_1383 *-commutative_binary64_1373 flip3-+_binary64_1445 flip-+_binary64_1416 pow1/3_binary64_1524
Counts
4 → 719
Calls

8 calls:

80.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 x)) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x)))))
25.0ms
(/.f64 (cbrt.f64 (sqrt.f64 x)) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x))))
8.0ms
(/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x)))
1.0ms
(cbrt.f64 x)
0.0ms
(cbrt.f64 (sqrt.f64 x))

series586.0ms (0.5%)

Counts
4 → 26
Calls

4 calls:

333.0ms
(/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x)))
100.0ms
(/.f64 (cbrt.f64 (sqrt.f64 x)) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x))))
79.0ms
(cbrt.f64 x)
73.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 x)) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 x)))))
Compiler

Compiled 664 to 522 computations (21.4% saved)

simplify311.0ms (0.3%)

Algorithm
egg-herbie
Counts
745 → 745
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
0492627753
1492627753

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(cbrt.f64 (sqrt.f64 x))
0.2b
(*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1)))
0.2b
(/.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 x)))
0.1b
(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 x)) 5) (*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1)))) (/.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 x))))
4.6b
(/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 x)) 5) (*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1))))
14.7b
(cbrt.f64 (+.f64 (*.f64 x x) 1))
14.7b
(cbrt.f64 (+.f64 (*.f64 x x) 1))
14.7b
(cbrt.f64 (+.f64 (*.f64 x x) 1))

rewrite46.0ms (0%)

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod_binary64_1473
18×cbrt-div_binary64_1474 unpow-prod-down_binary64_1521
17×add-exp-log_binary64_1480
15×add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
13×times-frac_binary64_1448 associate-/l*_binary64_1387
flip3-+_binary64_1445 flip-+_binary64_1416
associate-/r/_binary64_1388
add-cbrt-cube_binary64_1478
sqrt-prod_binary64_1458 div-exp_binary64_1493
add-log-exp_binary64_1481 frac-times_binary64_1452 pow1_binary64_1503
pow1/3_binary64_1524 prod-exp_binary64_1491
associate-*r/_binary64_1384 cbrt-undiv_binary64_1476 pow-exp_binary64_1510 sqr-pow_binary64_1414 associate-*l/_binary64_1385 pow-to-exp_binary64_1511
associate-/r*_binary64_1386 cbrt-unprod_binary64_1475 div-inv_binary64_1439 clear-num_binary64_1441 frac-2neg_binary64_1453
Counts
4 → 92
Calls

8 calls:

17.0ms
(/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 x)) 5) (*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
0.0ms
(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 x)) 5) (*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1)))) (/.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 x))))

series521.0ms (0.4%)

Counts
4 → 45
Calls

4 calls:

172.0ms
(/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 x)) 5) (*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1))))
119.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
117.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
113.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
Compiler

Compiled 1763 to 1351 computations (23.4% saved)

simplify129.0ms (0.1%)

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (94.0ms)

IterNodesCost
048843137
148843137

prune48.9s (41%)

Pruning

754 alts after pruning (744 fresh and 10 done)

PrunedKeptTotal
New7895221311
Fresh24222246
Picked000
Done11011
Total8147541568
Error
0b
Counts
1568 → 754
Compiler

Compiled 48304 to 25168 computations (47.9% saved)

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 1 (+.f64 x (/.f64 1 x)))
0.0b
(+.f64 x (/.f64 1 x))
0.0b
(+.f64 x (/.f64 1 x))
0.1b
(/.f64 1 (+.f64 x (/.f64 1 x)))

rewrite19.0ms (0%)

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity_binary64_1442
18×times-frac_binary64_1448
16×add-exp-log_binary64_1480
13×add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477
10×distribute-lft-out_binary64_1393
associate-/r*_binary64_1386 div-inv_binary64_1439 rec-exp_binary64_1492
cosh-undef_binary64_1636
add-cbrt-cube_binary64_1478 add-log-exp_binary64_1481
associate-/l*_binary64_1387 pow1_binary64_1503
associate-/r/_binary64_1388 flip3-+_binary64_1445 flip-+_binary64_1416 div-exp_binary64_1493
inv-pow_binary64_1527 cbrt-undiv_binary64_1476 sum-log_binary64_1533 clear-num_binary64_1441 1-exp_binary64_1486 +-commutative_binary64_1372 pow-flip_binary64_1516 frac-2neg_binary64_1453
Counts
2 → 59
Calls

4 calls:

8.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))
6.0ms
(+.f64 x (/.f64 1 x))
0.0ms
(+.f64 x (/.f64 1 x))
0.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))

series65.0ms (0.1%)

Counts
2 → 18
Calls

2 calls:

41.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))
24.0ms
(+.f64 x (/.f64 1 x))
Compiler

Compiled 177 to 153 computations (13.6% saved)

simplify99.0ms (0.1%)

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
04899953
14899953

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))
0.0b
(-.f64 (/.f64 -1 x) x)
0.0b
(-.f64 (/.f64 -1 x) x)
0.1b
(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))

rewrite30.0ms (0%)

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt_binary64_1464
72×times-frac_binary64_1448
59×*-un-lft-identity_binary64_1442
35×add-cube-cbrt_binary64_1477
24×difference-of-squares_binary64_1411
21×distribute-lft-neg-in_binary64_1399 distribute-rgt-neg-in_binary64_1400
12×distribute-lft-out--_binary64_1394
10×associate-/l*_binary64_1387
neg-mul-1_binary64_1438
associate-/r*_binary64_1386
add-cbrt-cube_binary64_1478 add-log-exp_binary64_1481 add-exp-log_binary64_1480
cancel-sign-sub-inv_binary64_1408
associate-/r/_binary64_1388 flip3--_binary64_1446 flip--_binary64_1417 pow1_binary64_1503
cbrt-undiv_binary64_1476 div-inv_binary64_1439 sub-neg_binary64_1435 clear-num_binary64_1441 frac-2neg_binary64_1453 diff-log_binary64_1534 distribute-frac-neg_binary64_1405 div-sub_binary64_1447 neg-sub0_binary64_1437 div-exp_binary64_1493
Counts
2 → 109
Calls

4 calls:

11.0ms
(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))
8.0ms
(-.f64 (/.f64 -1 x) x)
0.0ms
(-.f64 (/.f64 -1 x) x)
0.0ms
(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))

series74.0ms (0.1%)

Counts
2 → 18
Calls

2 calls:

42.0ms
(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))
32.0ms
(-.f64 (/.f64 -1 x) x)
Compiler

Compiled 196 to 172 computations (12.2% saved)

simplify77.0ms (0.1%)

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049592384
149592384

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(/.f64 1 (+.f64 (*.f64 x x) 1))
0.3b
(cbrt.f64 (sqrt.f64 x))
0.3b
(cbrt.f64 (sqrt.f64 x))
0.3b
(*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
1.3b
(*.f64 (/.f64 1 (+.f64 (*.f64 x x) 1)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))
6.1b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 1 (+.f64 (*.f64 x x) 1)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))))

rewrite56.0ms (0%)

Algorithm
rewrite-expression-head
Rules
99×add-exp-log_binary64_1480
63×prod-exp_binary64_1491
35×add-cbrt-cube_binary64_1478
33×cbrt-unprod_binary64_1475
30×pow1_binary64_1503
18×pow-prod-down_binary64_1513
17×add-sqr-sqrt_binary64_1464
16×associate-*l*_binary64_1383
14×*-un-lft-identity_binary64_1442
13×add-cube-cbrt_binary64_1477
12×div-exp_binary64_1493
11×times-frac_binary64_1448
cbrt-undiv_binary64_1476 cbrt-prod_binary64_1473 1-exp_binary64_1486 rec-exp_binary64_1492
add-log-exp_binary64_1481
unswap-sqr_binary64_1410
associate-*r*_binary64_1382 associate-/r/_binary64_1388 *-commutative_binary64_1373 pow1/3_binary64_1524 associate-*l/_binary64_1385
associate-*r/_binary64_1384 div-inv_binary64_1439 flip3-+_binary64_1445 flip-+_binary64_1416
Counts
4 → 109
Calls

8 calls:

23.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 1 (+.f64 (*.f64 x x) 1)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))))
19.0ms
(*.f64 (/.f64 1 (+.f64 (*.f64 x x) 1)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
0.0ms
(*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))

series328.0ms (0.3%)

Counts
4 → 24
Calls

4 calls:

101.0ms
(*.f64 (/.f64 1 (+.f64 (*.f64 x x) 1)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))
85.0ms
(cbrt.f64 x)
76.0ms
(cbrt.f64 x)
66.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 1 (+.f64 (*.f64 x x) 1)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))))
Compiler

Compiled 656 to 510 computations (22.3% saved)

simplify94.0ms (0.1%)

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
048551651
148551651

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(cbrt.f64 (sqrt.f64 x))
0.2b
(cbrt.f64 (sqrt.f64 (cbrt.f64 x)))
0.1b
(*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (fabs.f64 (cbrt.f64 x))))
0.0b
(sqrt.f64 (cbrt.f64 x))
0.5b
(cbrt.f64 x)
0.6b
(cbrt.f64 (fabs.f64 (cbrt.f64 x)))
1.4b
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 (cbrt.f64 x)))))
6.1b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 (cbrt.f64 x))))))

rewrite77.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
188×times-frac_binary64_1448
114×cbrt-prod_binary64_1473
83×add-sqr-sqrt_binary64_1464
82×add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
57×add-exp-log_binary64_1480
54×sqrt-prod_binary64_1458
45×associate-*r*_binary64_1382
40×associate-/r*_binary64_1386
29×add-cbrt-cube_binary64_1478
21×cbrt-unprod_binary64_1475 prod-exp_binary64_1491
18×cbrt-undiv_binary64_1476 div-exp_binary64_1493
pow1_binary64_1503
div-inv_binary64_1439
add-log-exp_binary64_1481
pow-prod-down_binary64_1513
associate-/r/_binary64_1388 pow1/3_binary64_1524
associate-*r/_binary64_1384 clear-num_binary64_1441 associate-/l*_binary64_1387 associate-*l*_binary64_1383 *-commutative_binary64_1373 frac-2neg_binary64_1453 unswap-sqr_binary64_1410
Counts
4 → 200
Calls

8 calls:

28.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 (cbrt.f64 x))))))
17.0ms
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 (cbrt.f64 x)))))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 (fabs.f64 (cbrt.f64 x)))
0.0ms
(sqrt.f64 (cbrt.f64 x))

series756.0ms (0.6%)

Counts
4 → 24
Calls

4 calls:

290.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 (cbrt.f64 x))))))
279.0ms
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (/.f64 (+.f64 (*.f64 x x) 1) (cbrt.f64 (sqrt.f64 (cbrt.f64 x)))))
108.0ms
(cbrt.f64 (fabs.f64 (cbrt.f64 x)))
78.0ms
(cbrt.f64 x)
Compiler

Compiled 1114 to 914 computations (18% saved)

simplify133.0ms (0.1%)

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049137811
149137811

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (fabs.f64 (cbrt.f64 x))))
0.1b
(sqrt.f64 (sqrt.f64 x))
0.1b
(sqrt.f64 (sqrt.f64 x))
0.0b
(sqrt.f64 (cbrt.f64 x))
0.5b
(cbrt.f64 x)
0.6b
(cbrt.f64 (fabs.f64 (cbrt.f64 x)))
1.2b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 (cbrt.f64 x)))))
6.1b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 (cbrt.f64 x))))))

rewrite83.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
90×add-exp-log_binary64_1480
60×cbrt-unprod_binary64_1475 prod-exp_binary64_1491
57×pow1_binary64_1503
40×add-cbrt-cube_binary64_1478
39×pow-prod-down_binary64_1513
cbrt-undiv_binary64_1476 cbrt-prod_binary64_1473 add-sqr-sqrt_binary64_1464 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442 div-exp_binary64_1493
add-log-exp_binary64_1481
associate-*r/_binary64_1384
associate-*r*_binary64_1382 associate-*l*_binary64_1383 *-commutative_binary64_1373 pow1/3_binary64_1524 associate-*l/_binary64_1385
Counts
4 → 98
Calls

8 calls:

41.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 (cbrt.f64 x))))))
26.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 (cbrt.f64 x)))))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 (fabs.f64 (cbrt.f64 x)))
0.0ms
(sqrt.f64 (cbrt.f64 x))

series759.0ms (0.6%)

Counts
4 → 24
Calls

4 calls:

299.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 (cbrt.f64 x))))))
265.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (fabs.f64 (cbrt.f64 x)))) (*.f64 (/.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 x))) (+.f64 (*.f64 x x) 1)) (cbrt.f64 (sqrt.f64 (cbrt.f64 x)))))
108.0ms
(cbrt.f64 (fabs.f64 (cbrt.f64 x)))
86.0ms
(cbrt.f64 x)
Compiler

Compiled 1186 to 938 computations (20.9% saved)

simplify95.0ms (0.1%)

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049754393
149754393

prune46.7s (39.2%)

Pruning

936 alts after pruning (922 fresh and 14 done)

PrunedKeptTotal
New444239683
Fresh56683739
Picked000
Done11415
Total5019361437
Error
0b
Counts
1437 → 936
Compiler

Compiled 11323 to 4607 computations (59.3% saved)

simplify1.1s (0.9%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0585567922

regimes8.0s (6.7%)

Compiler

Compiled 76149 to 47550 computations (37.6% saved)

bsearch0.0ms (0%)

regimes27.0ms (0%)

Compiler

Compiled 23 to 26 computations (-13% saved)

bsearch22.0ms (0%)

Steps
ItersRangePoint
8
0.0089137966523863
50.9956862610501
1.0239732575115408
10
-186490513025.27682
-0.03592090154576951
-0.9963031824001185
Compiler

Compiled 1 to 1 computations (0% saved)

regimes8.0ms (0%)

Compiler

Compiled 6 to 9 computations (-50% saved)

bsearch2.0ms (0%)

Compiler

Compiled 23 to 18 computations (21.7% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02730
12730

end0.0ms (0%)

sample1.0s (0.9%)

Algorithm
intervals
Results
183.0ms8000×body128valid
Compiler

Compiled 38076 to 23781 computations (37.5% saved)

Profiling

Loading profile data...